k-Harmonic immersion and submersion into a sphere

Details k-Harmonic immersion and submersion into a sphere k-Harmonic immersion and submersion into a sphere

2010-10-25

arxiv.org/abs/1010.5106v2

Mathematics

Differential Geometry

13 pages

Scientific paper

J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, We study k-harmonic immersion into a sphere, and get the rerationship between radious and "k" of k-harmonic. And we also consider k-harmonic submersion, and genelarize Oniciuc's results. Futhermore we construct non harmonic k-harmonic by Hopf map.

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